Panels of standard thickness having regularly-spaced holes have come into wide use to provide support for a variety of specialized brackets adapted to engage these holes. A piece of so-called "perfboard" equipped with these brackets can be used for the display of merchandise, for the storage of tools and miscellaneous items, and is easily adapted to particular items of odd configuration. Many of these standard brackets merely hook into the holes, and are thus vulnerable to jostling. My prior U.S. Pat. No. 3,545,711 provides an arrangement for securing a bracket positively to the perfboard, thus eliminating the possibility of accidental disengagement. In the arrangement disclosed in this patent, overlapped plates are each equipped with offsets adapted to engage the holes of the perfboard when the plate is in a position generally perpendicular to the surface of the board. As the units are then laid flat against the board, they are secured together so that they are no longer disengageable. This arrangement has been very satisfactory, but a need has been recognized to facilitate the installation of the overlapped plates and the threaded member that secures them in position. The need for alignment of the holes in the two plates so that the screw can be installed requires somewhat more attention than is desirable. The present invention provides a modified configuration for the outer plate which removes this problem entirely, and also provides further developments in the construction of brackets for special purposes that utilize the basic assembly shown in the above patent.